The 19-year-old, who had yet to compete in the Games, provided a urine sample, which was sent to a World Anti Doping Agency (WADA)-accredited laboratory for analysis.
The sample was found to contain the prohibited substance Furosemide, the EOC said in a statement.
"Mr Zeneli was therefore charged with an Anti-Doping Rule Violation, and it was determined by the EOC Executive Committee on the recommendation of the EOC's Committee for Legal, Eligibility, Disciplinary and Doping Matters that he is suspended from participation in the European Games," the statement read.
Baku 2015 European Games
Watch: Athlete wins gold, sportingly carries injured opponent off mat
"Further anti-doping procedures will be conducted by the competent international organisations."
The inaugural European Games in the Azeri capital of Baku runs until June 28.
Legends live on – Derartu Tulu and the 10,000m final for all of Africa
Legends Live On - Episode 3: Three-time Olympic judo champion Nomura Tadahiro